Thanks for the suggestions, everyone.
I methodically pulled all the fuses from the PD4045. Interestingly enough the fridge has no fuse in that panel. I am able to reproduce the issue by putting the fridge on DC power.
I shorted the battery bypass and I still get the issue.
I did clean and reconnect battery contacts and the chassis grounding wires.
I have not been able to locate an inline circuit breaker.
I think I could be having a battery issue or maybe there is a circuit breaker under the bathroom sink that is out of reach/view. When the power cuts I hear a thunk from the lifeline AGM battery. This is a sound I usually hear when the battery is low and bulk charging starts. I was told by lifeline that this sound is normal when charging.
The power can be out for several seconds. When it comes back on I hear a little click under the sink. Could that be a circuit breaker?
It's going to be raining here for the next few hours so I'm going to take a break before pulling the batteries. I think I'll connect them one at a time to see if the problem follows a specific battery. If it's a battery issue, I doubt it's both of them.
At this point I really hope it's a battery. I have no idea how I'm going to get access to the wiring under the bathroom sink.